/// <summary>开方</summary>
static internal BigNumber Sqrt(BigNumber value, int precision)
{
if (!value.IsPlus)
{
throw new ExpressionException("只有正数才有开平方运算");
}
List <int> div = new List <int>();
int index = 0;
int resultIntCount = (value.IntPart.Count + 1) / 2;
List <int> result = GetFirstDiv(value, ref div, ref index);
div = FirstTry(result, div);
div.AddRange(GetNewTwoDiv(value, ref index));
BigCalculate.RemoveStartZero(div);
//考虑精度的计算
while (true)
{
div = TryDiv(div, result);
if (result.Count - resultIntCount >= precision)
{
break;
}
div.AddRange(GetNewTwoDiv(value, ref index));
BigCalculate.RemoveStartZero(div);
}
return(new BigNumber(result.GetRange(0, resultIntCount), result.GetRange(resultIntCount, result.Count - resultIntCount), true));
}
/// <summary>第一次用开方尝试</summary>
private static List <int> FirstTry(List <int> result, List <int> div)
{
int tryDiv = BigNumber.Max / 2;
int low = 1;
int top = BigNumber.Max - 1;
//第一位数是1
//第一用平方试商
while (true)
{
if (BigCalculate.CompareList(new List <int>()
{
1
}, div) == 0)
{
div = BigCalculate.IntMinus(div, new List <int>()
{
1
});
result.Add(1);
break;
}
//连9都小了，那么就是9
if (BigCalculate.CompareList(BigCalculate.Multiply(BigNumber.Max - 1, BigNumber.Max - 1), div) == -1)
{
div = BigCalculate.IntMinus(div, BigCalculate.Multiply(BigNumber.Max - 1, BigNumber.Max - 1));
result.Add(BigNumber.Max - 1);
break;
}
int c = BigCalculate.CompareList(BigCalculate.Multiply(tryDiv, tryDiv), div);
//商大了
if (c == -1)
{
low = tryDiv;
tryDiv = (low + top) / 2;
}
else if (c == 1) //商小了
{
top = tryDiv;
tryDiv = (low + top) / 2;
}
else //刚好相等
{
div.Clear();
result.Add(tryDiv);
break;
}
if (low + 1 == top)
{
div = BigCalculate.IntMinus(div, BigCalculate.Multiply(low, low));
result.Add(low);
break;
}
}
return(div);
}
/// <summary>执行一次试商的运算</summary>
/// <param name="div">已经加组的被除数</param>
/// <param name="result">已生成的结果</param>
static List <int> TryDiv(List <int> div, List <int> result)
{
int i = BigNumber.Max / 2;
int low = 0;
int top = BigNumber.Max - 1;
//连1都大了,那么商为0，除数不变
if (CompartDiv(1, result, div) == 1)
{
result.Add(0);
return(div);
}
//连9999都小了
if (CompartDiv(BigNumber.Max - 1, result, div) == -1)
{
List <int> r = BigCalculate.IntMinus(div, CalDiv(BigNumber.Max - 1, result));
result.Add(BigNumber.Max - 1);
return(r);
}
while (true)
{
int c = CompartDiv(i, result, div);
//商大了
if (c == 1)
{
top = i;
i = (low + top) / 2;
}
//商小了
else if (c == -1)
{
low = i;
i = (low + top) / 2;
}
//刚好相等
else
{
//div.Clear();
result.Add(i);
return(new List <int>());
}
//已找到合适的商
if (low + 1 == top)
{
List <int> r = BigCalculate.IntMinus(div, CalDiv(low, result));
result.Add(low);
return(r);
}
}
}
/// <summary>计算x(x+20*result)的值</summary>
static List <int> CalDiv(int x, List <int> result)
{
List <int> result20 = BigCalculate.Multiply(new List <int>()
{
BigNumber.Max * 2
}, result);
List <int> add = BigCalculate.IntAdd(new List <int>()
{
x
}, result20, 0);
List <int> r = BigCalculate.Multiply(new List <int>()
{
x
}, add);
return(r);
}
/// <summary>返回0.00001这样的数小数点后、有效数前有几个零</summary>
internal int GetPrecision(int value)
{
if (value == 0)
{
BigCalculate.RemoveStartZero(IntPart);
if (IntPart.Count == 1 && IntPart[0] == 0)
{
if (DecimalPart.Count == 0)
{
return(0);
}
for (int i = 0; i < DecimalPart.Count; i++)
{
if (DecimalPart[i] != 0)
{
return(i);
}
}
return(DecimalPart.Count);
}
return(0);
}
else
{
if (IntPart.Count == 1 && IntPart[0] == 1)
{
if (DecimalPart.Count == 0)
{
return(0);
}
for (int i = 0; i < DecimalPart.Count; i++)
{
if (DecimalPart[i] != 0)
{
return(i);
}
}
return(DecimalPart.Count);
}
return(0);
}
}
/// <summary>识别出一个大数，返回值为这个是不是正数</summary>
public static bool GetBigNumber(string text, List <int> intPart, List <int> decimalPart)
{
ValidateNumber(text);
bool isPlus = true;
int haveSym = 0;
if (text[0] == '-')
{
isPlus = false;
haveSym = 1;
}
else if (text[0] == '+')
{
haveSym = 1;
}
int pointIndex = text.IndexOf('.');
//有小数点
if (pointIndex != -1)
{
int i = 0;
if ((pointIndex - haveSym) % BigNumber.OneCount != 0)
{
intPart.Add(Convert.ToInt32(text.Substring(haveSym, (pointIndex - haveSym) % BigNumber.OneCount)));
}
for (; i < (pointIndex - haveSym) / BigNumber.OneCount; i++)
{
intPart.Add(Convert.ToInt32(text.Substring(haveSym + i * BigNumber.OneCount + (pointIndex - haveSym) % BigNumber.OneCount, BigNumber.OneCount)));
}
i = pointIndex + 1;
while (i < text.Length)
{
if (text.Length - i >= BigNumber.OneCount)
{
decimalPart.Add(Convert.ToInt32(text.Substring(i, BigNumber.OneCount)));
}
else
{
decimalPart.Add(Convert.ToInt32(text.Substring(i, (text.Length - i) % BigNumber.OneCount).PadRight(BigNumber.OneCount, '0')));
}
i += BigNumber.OneCount;
}
}
//没有小数点
else
{
if ((text.Length - haveSym) % BigNumber.OneCount != 0)
{
intPart.Add(Convert.ToInt32(text.Substring(haveSym, (text.Length - haveSym) % BigNumber.OneCount)));
}
for (int i = 0; i < (text.Length - haveSym) / BigNumber.OneCount; i++)
{
intPart.Add(Convert.ToInt32(text.Substring(haveSym + i * BigNumber.OneCount + (text.Length - haveSym) % BigNumber.OneCount, BigNumber.OneCount)));
}
}
BigCalculate.RemoveStartZero(intPart);
if (intPart.Count == 0)
{
intPart.Add(0);
}
return(isPlus);
}
/// <summary>对除数进行比较</summary>
static int CompartDiv(int x, List <int> result, List <int> div)
{
return(BigCalculate.CompareList(CalDiv(x, result), div));
}
/// <summary>指定精确的除法</summary>
public static BigNumber Division(BigNumber dividend, BigNumber divisor, int precision)
{
return(BigCalculate.Division(dividend, divisor, precision));
}
public static BigNumber operator /(BigNumber a, BigNumber b)
{
return(BigCalculate.Division(a, b));
}
public static BigNumber operator *(BigNumber a, BigNumber b)
{
return(BigCalculate.Multiply(a, b));
}
public static BigNumber operator -(BigNumber a, BigNumber b)
{
return(BigCalculate.Minus(a, b));
}
public static BigNumber operator +(BigNumber a, BigNumber b)
{
return(BigCalculate.Add(a, b));
}
static int ComparePlus(BigNumber one, BigNumber two)
{
BigCalculate.RemoveStartZero(one.IntPart);
BigCalculate.RemoveStartZero(two.IntPart);
int minDecimalLength = one.DecimalPart.Count < two.DecimalPart.Count ? one.DecimalPart.Count : two.DecimalPart.Count;
//通过正数的长短比较
if (one.IntPart.Count > two.IntPart.Count)
{
return(1);
}
else if (one.IntPart.Count < two.IntPart.Count)
{
return(-1);
}
else
{
//从最高位依次比较
for (int i = 0; i < one.IntPart.Count; i++)
{
if (one.IntPart[i] > two.IntPart[i])
{
return(1);
}
else if (one.IntPart[i] < two.IntPart[i])
{
return(-1);
}
}
//比较小数部分，行判断是否有小数位
if (one.DecimalPart.Count == 0 && two.DecimalPart.Count != 0)
{
return(-1);
}
else if (one.DecimalPart.Count != 0 && two.DecimalPart.Count == 0)
{
return(1);
}
else if (one.DecimalPart.Count == 0 && two.DecimalPart.Count == 0)
{
return(0);
}
else
{
for (int i = 0; i < minDecimalLength; i++)
{
if (one.DecimalPart[i] > two.DecimalPart[i])
{
return(1);
}
else if (one.DecimalPart[i] < two.DecimalPart[i])
{
return(-1);
}
}
if (one.DecimalPart.Count > two.DecimalPart.Count)
{
return(1);
}
else if (one.DecimalPart.Count < two.DecimalPart.Count)
{
return(-1);
}
}
return(0);
}
}